Kaplan MCAT General Chemistry Review

DEFINITION OF RATE

If we consider a generic reaction, 2A + B C, in which one mole of C is produced from every two moles of A and one mole of B, we can describe the rate of this reaction in terms of either the disappearance of reactants over time or the appearance of products over time. Because the reactants, by definition, are being consumed in the process of formation of the products, we place a minus sign in front of the rate expression in terms of reactants. For the previous reaction, the rate of the reaction with respect to A is -[A]/t, with respect to B is -[B]/t, and with respect to C is [C]/t. You’ll notice that the stoichiometric coefficients for the reaction are not equal, and this tells you that the rates of change of concentrations are not equal. Because two moles of A are consumed for every mole of B consumed, rate _-[A] = 2 rate_-[B]. Furthermore, for every two moles of A consumed, only one mole of C is produced; thus, we can say that the rate_-[A] = 2 rate_[C]. Based on the stoichoimetry, you can see that the rate of consumption of B is equal to the rate of production of C. To show a standard rate of reaction in which the rates with respect to all reaction species are equal, the rate of concentration change of each species should be divided by the species’ stoichiometric coefficient:

And for the general reaction aA + bB cC + dD:

Rate is expressed in the units of moles per liter per second (mol/L/s) or molarity per second (M/s).

DETERMINATION OF RATE LAW

Here’s something you can take to the bank (that is, to the MCAT testing center): In the Physical Sciences section of the MCAT, it is extremely unlikely that the test maker will give you a reaction equation that you can merely look at and write the correct rate law. Therefore, on the MCAT, whenever you are asked to determine the rate law for a reaction in which you are given the net equation, the first thing you will do is look for experimental data.

MCAT Expertise

Remember that the stoichiometric coefficients for the overall reaction will most likely be different from those for the rate-determining step and will, therefore, not be the same as the order of the reaction.

However, we’re getting ahead of ourselves, so let’s start with the basics. For nearly all forward, irreversible reactions, the rate is proportional to the product of the concentrations of the reactants, each raised to some power. For the general reaction

aA + bB cC + dD

the rate is proportional to [A]^x[B]^y. By including a proportionality constant, k, we can say that rate is determined according to the following equation:

rate = k[A]^x[B]^y

This expression is called the rate law for the general reaction shown here, where k is the reaction rate coefficient or rate constant. Rate is always measured in units of concentration over time; that is, molarity/second. The exponents x and y (or x, y, and z, if there are three reactants, etc.) are called the orders of the reaction: x is the order with respect to reactant A, and y is order with respect to reactant B. The overall order of the reaction is the sum of x + y (+ z...). These exponents may be integers, fractions, or zero and must be determined experimentally. The MCAT will focus almost entirely on zero-, first-, second-, and third-order reactions only. Furthermore, in most cases, the exponents will be integers.

Before we go any further in our consideration of rate laws, we must offer a few warnings about common traps that students often fall into. The first—and most common—is the mistaken assumption that the orders of a reaction are the same as the stoichiometric coefficients in the balanced overall equation. Pay close attention to this: The values of x and y usually aren’t the same as the stoichiometric coefficients . The orders of a reaction are usually must be determined experimentally. There are only two cases in which you can take stoichiometric coefficients as the orders of reaction. The first is when the reaction mechanism is a single step and the balanced “overall” reaction is reflective of the entire chemical process. The second is when the complete reaction mechanism is given and the rate-determining step is indicated. The stoichiometric coefficients on the reactant side of the rate-determining step are the orders of the reaction. Occasionally, even this can get a little complicated when the rate-determining step involves an intermediate as a reactant, in which case you must derive the intermediate molecule’s concentration by the law of mass action (that is, the equilibrium constant expression) for the step that produced it.

MCAT Expertise

Note that the exponents in the rate law are not equal to the stoichiometric coefficients, unless the reaction actually occurs via a single-step mechanism. Also, note that product concentrations never appear in a rate law. Don’t fall into the common trap of confusing the rate law with an equilibrium expression!

The second trap to be wary of is mistaking the equilibrium aspect of the law of mass action for the kinetic aspect. The equations for the two aspects do look similar, and if you’re not alert, you may mistake one for the other or use one when you should be using the other. The expression for equilibrium includes the concentrations of all the species in the reaction, both reactants and products. The expression for chemical kinetics, the rate law expression, includes only the reactants. K_eq tells you where the reaction’s equilibrium position lies. The rate tells you how quickly the reaction will get there (that is, reach equilibrium).

The third trap we need to warn you about is regarding the rate constant, k. Technically speaking, it’s not a constant, because its particular value for any specific chemical reaction will depend on the activation energy for that reaction and the temperature at which the reaction takes place. However, for a specific reaction at a specific temperature, the rate coefficient is constant. For a reversible reaction, the K_eq is equal to the ratio of the rate constant, k, for the forward reaction, divided by the rate constant, k_-1, for the reverse reaction (see Chapter 6, Thermochemistry).

The fourth and final trap we need to warn you about is that the notion and principles of equilibrium apply to the system only at the end of the reaction; that is, the system has reached equilibrium. The reaction rate, while it theoretically can be measured at any time, is usually measured at or near the beginning of the reaction to minimize the effects of the reverse reaction.